指数维

结论：Bolton指数在维、汉族错（牙合）患者中分布有差异。

Conclusion : Significant difference can be found in both distributions of male , female patients and comparisions of Bolton index between Uigur and Han .

用大气湍流资料计算Lyapunov指数和分数维

Computation of Lyapunov exponent and fractal dimension by using atmospheric turbulent data

利用Lyapunov指数和容量维分析永磁同步电机仿真中的混沌现象

Analyzing Chaotic Phenomenon in Permanent-Magnet Synchronous Motors with Lyapunov Exponent and Capacity Dimension

Hurst指数与容量维在油气检测中的应用

Application of Hurst exponent and volume dimension to hydrocarbon prediction

计算了模型产生的股价时间序列的Lyapunov指数和关联维，并对其进行主分量分析。

The Lyapunov exponent and correlative dimension of the stock price time series created from the model are calculated , and a principal component analysis is carried out .

再次，提出了在实验条件下的永磁同步电动机的混沌研究方法。基于时间序列重构了永磁同步电动机的状态空间，并给出了基于时间序列的Poincare映射、Lyapunov指数和容量维的数值算法。

Besides , the numerical algorithms for calculating Poincare map , Lyapunov exponents and capacity dimensions are also proposed for studying the chaotic characteristics of the PMSM .

本文简要介绍并分析了现有对非线性时间序列进行数值分析的手段，包括Lyapunov指数、分数维、测度熵以及多种复杂性测度等。

In this paper , the present methods of data analyzing on nonlinear time sequence is introduced at first , which include Lyapunov exponent , partial dimension , measure entropy and several complexity measures .

通过计算机模拟和理论分析对它的奇怪吸引子、最大Lyapunov指数、分数维、频谱、功率谱和分岔等非线性动力学特性进行了深入研究。

The nonlinear dynamic properties of the system such as strange attractor , the largest Lyapunov index , fractal dimension , spectrum , power spectrum and bifurcation are researched via theoretical analysis and digital simulation .

给出了一种适合于一般混沌系统Lyapunov指数和容量维计算的数值算法，并首次应用于永磁同步电机混沌现象的分析。

This paper proposed a numerical algorithm to compute the Lyapunov exponent and capacity dimension for nonlinear chaotic system , and first applies it to analyse the chaotic phenomena of permanent magnet synchronous motors ( PMSM ) .

该方法首先研究了噪声对嵌入相空间中两点距离的影响，然后根据最大Lyapunov指数在不同维嵌入相空间中不变的性质，提出了从时间序列同时估计最大Lyapunov指数和噪声水平的方法。

The influence of noise on the distance of two points in an embedding phase space is researched , and then our algorithm is proposed based on the invariant of the largest Lyapunov exponent in different dimensional embedding phase spaces .

其次分析了其混沌时间序列的Lyapunov指数、关联维、Kolmogorov熵等动力学特性.由于该混沌动力系统参数复杂，动力学行为受参数影响敏感，因此在密码学中有广阔的应用前景。

Second , an analysis of the Lyapunov exponent , correlation dimension , Kolmogorov entropy of the chaotic time series are made . The chaotic dynamic system is difficult to be decrypted because it has more parameters and it is sensitive to the parameters .

该文通过Hurst指数、分形维、稳定指数和分形差分参数4种方法对中国股票市场的分形结构进行实证研究。

This paper probes and discusses the fractal structure characterized by self-similarity and long memory . It conducts empirical research on Chinese stock market by four kinds of fractal parameters , i.e. , Hurst index , fractal dimension , stable index and fractional difference parameter .

非线性系统指数型降维观测器设计

The exponential reduced - order observers for Nonlinear Systems

大气湍流的间歇性&Lyapunov特征指数和分数维的应用

The intermittency of atmospheric turbulence - application of Lyapunov exponents and fractal dimension

正的特征指数和分数维可以定量表征湍流的间歇性。

The characteristics of chaos , are that positive characteristic exponents and fractional dimension can quantitatively express the turbulent intermittency .

方法利用庞加莱截面、李雅普诺夫指数、关联维等工具分别对抛物方程和椭圆方程的非线性动力学行为进行描述。

Methods Nonlinear dynamical behavior of both parabolic equation and elliptic equation were investigated by several tools such as Poincare section , Lyapunov exponent , and correlation dimension .

给出了将图像分解为一系列具有不同奇异性指数和分数维的分形集合的分解算法。

According to the exponential formalism , the paper also presented an algorithm , in which the nature image can be decomposed in a serial fractal sets with different singularity exponent and fractal dimension .

运用混沌理论研究了冲击地压的特性，通过震级数据的Lyapunov指数和Kolmogorov容量维分析，得出冲击地压具有混沌特性的结论并描述了其动力模型的最少参数。

The chaos theory is used to research rockburst characteristic in the paper . According to the analysis of Lyapunov factor of level and the Kolmogorov capacity dimension , it is required that rockburst have chaos characteristic and minimum parameters of its dynamic model .

通过相图分析、李雅普诺夫指数分析和分维分析，本文得到了二维超声速自由剪切层流动由线性到非线性失稳过程的数学特征。

Upon the analyses on the phase mapping , Lyapunov exponents and fractal dimension , the mathematical feature of nonlinear instability development have been described .

草地和未利用地景观类型随着人类的开发利用和改造，集合度指数增加，形状指数和分维数值持续减小。

With the development of society , grassland and unused land landscape also tended to regular , and Aggregation Index increasing , Landscape Shape Index and Perimeters-Area Fractal Dimension Index decreasing .